{
  "id": "1510.01672",
  "version": "v1",
  "published": "2015-10-06T17:21:49.000Z",
  "updated": "2015-10-06T17:21:49.000Z",
  "title": "Numerical Ranges of the product of Operators",
  "authors": [
    "Hongke Du",
    "Chi-Kwong Li",
    "Kuo-Zhong Wang",
    "Yueqing Wang",
    "Ning Zuo"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study containment regions of the numerical range of the product of operators $A$ and $B$ such that $W(A)$ and $W(B)$ are line segments. It is shown that the containment region is equal to the convex hull of elliptical disks determined by the spectrum of $AB$, and conditions on $A$ and $B$ for the set equality holding are obtained. The results cover the case when $A$ and $B$ are self-adjoint operators extending the previous results on the numerical range of the product of two orthogonal projections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-06T17:21:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A60",
      "47A12"
    ],
    "keywords": [
      "numerical range",
      "study containment regions",
      "convex hull",
      "line segments",
      "results cover"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151001672D"
    }
  }
}